Translation:The young kindergarten teacher goes down to the water.
You confuse beta stage inconsistencies with "pedantic American-centrism" methinks. "Nursery teacher" and "nursery school teacher" are included as hints for "óvónő" essentially everywhere it appears in the course. (I don't know if the former is actually used anywhere; there's not a single occurrence of it in the Corpus of Contemporary American English.) If the option you prefer is missing in the translations in any specific instance, report it; there is, indeed, no need to "labour the point." I don't think I've ever seen "preschool teacher," which would probably be my candidate for the most sensible American quasi-equivalent.
I actually don't think there's much going on here about English dialect preference at all. "Kindergarten teacher" simply appears to be (here for example) the English translation one encounters for óvónő. The institution of pre-primary education in Hungry in which such individuals work lacks, I think, a precise analogue in the English-speaking world: https://en.wikipedia.org/wiki/Education_in_Hungary#Pre-primary_education. I wouldn't be surprised if this translation preference, such as it is, has more to do with the German history of the concept of kindergarten than anything about English particularly.
Fwiw, "kindergartens" is hardly a common term in the U.S. (the first pages of Google results seem to be dominated by New Zealand) and when used I think it's essentially a colloquial alternative for "kindergarten class" (i.e. a group of students assigned to a certain teacher).
Many thanks Piguy3 for your considered and informative reply. My frustration comes simply from Duolingo's dogmatic insistence on "kindergarten" and rejecting in big red type a perfectly reasonable alternative! I don't understand why this really excellent learning aid isn't a little more flexible in what it accepts: it shouldn't be that difficult to expand its "white list". Still, as you say, it is only a beta version at present.
Indeed, adding any one translation isn't too big an effort. It's the cumulative effect of all the additions for the thousands of sentences in the course and the fact that it's not difficult for the number of valid Hungarian translations of an English sentence to run into the thousands. With its flexible word order, Hungarian is a singularly difficult language to teach from or to within the Duolingo set-up.
I don't quite understand how an action in the present tense can be completed. Is it that it's expected to be completed, that it's expressing the intention of completing? As opposed to "is going to the water."
That said, I think "down to the water" is itself an idiomatic expression in English. If I'm on a beach, or near a river or whatever, and I'm walking toward the water, I'd probably say that I'm going down to the water. It's not so much part of the verb as part of the phrase "to the water." In English, that is.
You raise a good question about the present tense. But consider this: "She goes (down) to the river every Thursday." I think it's fair to say that we are talking here (in English) about completed trips each Thursday, not just about attempts at reaching the river that may or may not be completed each Thursday.
Also, bear in mind that English has a present perfect tense for describing completed actions: "She has gone (down) to the river". In contrast, Hungarian has no present perfect, and so relies on the prefix to give the sense of completion that can be expressed by the present perfect in English.
In other words, I think the question you raised about the present tense not showing completion is a fair observation about English, but perhaps not about Hungarian.